In a DIAL system, the received back scattered signal is a function of: the transmitted laser pulse energy; the speed of light; the laser pulse width; the telescope area (field of view); the range (inverse square law); the offline beam and online beam overlap and the field of view (i.e. the geometric form factor); the spectral response of the receiver optics; the plume transmission; the total atmospheric transmission; and the ground cover type.
One use of a two-line DIAL system is to estimate the concentration path length (CPL) of a fluid related plume. Therefore, the online wavelength is desirably selected such that it is only absorbed by the target molecule of the fluid and nothing else in the optical path. The offline wavelength is desirably selected such that it is not absorbed by the target molecule or any other anticipated molecules allow the optical path. More desirably, the online and offline wavelengths are selected such that the ratio of the geometric form factor, the spectral response of the receiver optics, and the surface reflectivity corresponding to the online and offline wavelengths are approximately the same. As may be seen in Equation 1, when this condition is met, these parameters may cancel out, simplifying calculation of the CPL.
                              CPL          =                                                                                                                                        ln                        ⁡                                                  (                                                                                                                    E                                ⁡                                                                  (                                                                                                            λ                                      Off                                                                        ,                                    R                                                                    )                                                                                            ⁢                                                                                                                          ⁢                                                                                                E                                  1                                                                ⁡                                                                  (                                                                      λ                                    On                                                                    )                                                                                            ⁢                                                                                                                          ⁢                                                              ξ                                ⁡                                                                  (                                                                      R                                    On                                                                    )                                                                                            ⁢                                                                                                                          ⁢                                                              ξ                                ⁡                                                                  (                                                                      λ                                    On                                                                    )                                                                                            ⁢                                                              ρ                                ⁡                                                                  (                                                                      λ                                    On                                                                    )                                                                                                                                                                                    E                                ⁡                                                                  (                                                                                                            λ                                      On                                                                        ,                                    R                                                                    )                                                                                            ⁢                                                                                                                          ⁢                                                                                                E                                  1                                                                ⁡                                                                  (                                                                      λ                                    Off                                                                    )                                                                                            ⁢                                                                                                                          ⁢                                                              ξ                                ⁡                                                                  (                                                                      R                                    Off                                                                    )                                                                                            ⁢                                                                                                                          ⁢                                                              ξ                                ⁡                                                                  (                                                                      λ                                    Off                                                                    )                                                                                            ⁢                                                              ρ                                ⁡                                                                  (                                                                      λ                                    Off                                                                    )                                                                                                                                              )                                                                    -                                                                                                                                  2                      ⁢                                                                        ∫                          0                          2                                                ⁢                                                                              (                                                                                          k                                ⁡                                                                  (                                                                                                            λ                                      On                                                                        ,                                    r                                                                    )                                                                                            -                                                              k                                ⁡                                                                  (                                                                                                            λ                                      Off                                                                        ,                                    r                                                                    )                                                                                                                      )                                                    ⁢                                                                                                          ⁢                                                      ⅆ                            r                                                                                                                                                                          2                ⁢                                  (                                                            σ                      ⁡                                              (                                                  λ                          On                                                )                                                              -                                          σ                      ⁡                                              (                                                  λ                          Off                                                )                                                                              )                                                      -                          RC                              t                -                bag                                                    ,                            Eq        .                                  ⁢                  (          1          )                    where λOn/Off is the online (or offline) peak wavelength, σ(λOn/Off) is the online (or offline) cross-section, E1(λOn/Off) is the online (or offline) transmitted laser pulse energy, R is the range/altitude/distance of the sensor to the target, E(λOn/Off,R) is the online (or offline) received laser pulse energy, ξ(ROn/Off) is the geometric form factor for the online (or offline) peak wavelength, ξ(λOn/Off) is the spectral response of the receiver optics for the online (or offline) peak wavelength, ρ(λOn/Off) is the background surface reflectance for the online (or offline) peak wavelength, k(λOn/Off,r) is the atmospheric attenuation coefficient for the online (or offline) peak wavelength, and Ct-bag is the target molecule concentration in the atmosphere.
In many cases, the dominating factor in DIAL system performance is the low signal relative to noise, or low Signal to Noise Ratio (SNR), and not electrical noise in the system. This problem may be especially acute when the SNR varies. In such situations the DIAL equation must be corrected to account for non-uniform variations and error (bias). The main source of these errors or non-uniform variations of the online and offline retuned signals are surface cover type spectral reflectivity variations and/or the misalignment of the online and offline beams (partially-overlapping beams). Partially overlapped beams may also lead to surface spectral reflectivity variations in the online and offline retuned signals. The online and offline wavelength desirably do not vary during the operation of the DAIL system. Therefore, the wavelengths are typically electronically locked at preselected wavelengths. However, in practice, these wavelengths may slightly vary and these variations may lead to spikes in cross-section and other undesirable interfering absorption effects. Furthermore, the estimation of the probability density function of plume points associated with a gas leak may not be practical.
Low surface cover type reflectivity applications result in low return online and offline signals and high surface cover type reflectivity applications result in high return is online and offline signals. When the returned signal is low relative to noise then the electrical noise dominates and this leads to low Signal to Noise Ration (SNR) and large Concentration Path Length (CPL) Variance, but the opposite is also true. When the returned signals are high relative to noise then the signal dominates and this leads to high SNR and low CPL Variance. Therefore, since the surface reflectivity varies from point to point and from region to region, so do the retuned signals and SNR.
However, in practice DIAL systems may be calibrated accordingly. Unfortunately, correcting for reflectivity variations due to ground surface cover type may be difficult in many situations. If these ground surface cover type reflectivity variations are not properly corrected, significant errors in CPL estimates of the target molecule may result, leading to false identification of plumes (or lack of plumes).
The present invention involves a method for improving the performance accuracy in DIAL by utilizing spectral and spatial information. Improved methods of the present invention may increase (probability) certainty of detection of plumes containing the target molecule. For example, these improved methods may be useful in identification of plumes generated by leaks in pipelines or storage tanks, plumes caused by spills and other contamination, and naturally occurring plumes such as gases emitted by volcanoes.